definitely 2 different types of tires for the 2 venues.
The Wilmington Mile, you want good concrete traction, need a hard start and a lot of acceleration. Drag radials.
Bonneville, 3 miles/7 miles of Salt, hard, but little grains on top. Wide tires with sand like salt underneath, bad for traction, that's why most like skinny tires, plenty of time to accelerate, better traction with more weight per sq inch.
expensive solution...